In a factorial hidden Markov model, there are multiple independent chains of hidden variables, which in this case are the current operating state of each appliance. At each time slice, there is also an observed variable conditional on the states of all of the corresponding hidden variables, which in the case is the premise-level power value. Below is a diagram of a factorial hidden Markov model.
- Z - hidden (latent) variable, subscript - time slice, superscript - variable number
- X - observed variable, subscript, time slice